Their complex algorithms and advanced mathematical theories probably would not mean much to anyone without a degree in computer science, but the work of two Massachusetts Institute of Technology professors has established the gold standard for safeguarding transactions on the Web.

Some 30 years after professors Shafi Goldwasser and Silvio Micali began working in the field of modern cryptography, the two were awarded the prestigious A.M. Turing Award Wednesday from the Association for Computing Machinery for their pioneering work on the kind of data encryption used to protect electronic commerce from malicious hackers and thieves.

“We are indebted to these recipients for their innovative approaches to ensuring security in the digital age,” said Vint Cerf, president of the association, the world’s largest education and scientific computing society.

The award, named for British computer scientist and World War II codebreaker A.M. Turing, has been compared to the Nobel Prize for the world of technology, and MIT professors or alumni have been recipients of the award nine other times. Goldwasser and Micali will share a $250,000 prize.

Goldwasser and Micali met in the 1980s while studying at the University of California Berkeley, where they began exploring how to keep information secret in an era of advanced computing. Over the years, they discovered new ways in which advanced mathematics could be used to encrypt documents and private information, ensuring more secure transmissions among multiple recipients.

They developed methods for secure transmissions that allow different parties to safely share all kinds of information over the Web without exposing it to prying eyes.

In a 1982 paper, the two devised ways to apply methods of cryptography, or security protocols that hide information, to guard digital data.

‘Mathematics, which is considered a dry thing, can enable our digital society.’

Basically, they came up with a scheme for embedding random encryptions to keep data secret.

The papers that Goldwasser and Micali have published together laid “the foundation for the security measures everywhere,” said Omer Reingold, a principal researcher at Microsoft Research in Mountain View, Calif., and a member of the ACM.

“They have turned cryptography from an art to a science,” he said. “It’s impossible to have any intelligent conversation about cryptography today without being fundamentally influenced by their work.”

During an interview at their offices at MIT’s Computer Science and Artificial Intelligence Laboratory, Goldwasser and Micali frequently spoke about their work in the abstract terms of theories and equations. Boiled to its essence, Goldwasser and Micali said they showed how mathematics underpins so much of the workings of the Web.

“These are the building blocks,” said Goldwasser. “Mathematics, which is considered a dry thing, can enable our digital society.”

By winning the A.M. Turing Award, Goldwasser and Micali join a list of prestigious computer scientists, including MIT professor Barbara Liskov for her her work creating computer programming languages and Charles Thacker for helping develop the personal computer and Ethernet.